Self-Assembly of Magnetic Spheres in Strong Homogeneous Magnetic Field

TL;DR

This paper theoretically investigates how spherical magnets self-assemble into chain structures under strong magnetic fields, revealing stable configurations and transition points for different numbers of magnets.

Contribution

It provides a detailed analysis of the self-assembly process of magnetic spheres, identifying stable structures and transition points using numerical and analytical methods.

Findings

Stable straight chains for N ≤ 26 magnets.

Formation of two touching chains for N ≥ 27.

Transition from two to three chains at N = 129.

Abstract

The self-assembly in two dimensions of spherical magnets in strong magnetic field is addressed theoretically. %% It is shown that the attraction and assembly of parallel magnetic chains is the result of a delicate interplay of dipole-dipole interactions and short ranged excluded volume correlations. %% Minimal energy structures are obtained by numerical optimization procedure as well as analytical considerations. For a small number of constitutive magnets $N_{\rm tot}\leq26$, a straight chain is found to be stable. In the regime of larger $N_{\rm tot}\geq27$, the magnets form \textit{two touching} chains with equally long tails at both ends. We succeed to identify the transition from \textit{two} to \textit{three} touching chains at $N_{\rm tot}=129$.